At about 60 mph the steering wheel shakes badly, i had the tires balanced, it didn't help?

possible a wheel alignment possibly from the rear wheels and loose/worn suspension rubbers

It sounds like you either:

1. wheels/tires that are not balanced properly (most likely)
2. bad wheel bearings (very dangerous)
3. Have a cylinder misfire
4. Have warped brake rotors

A tire/wheel shop should be able to narrow down the problem

I doubt these problems have anything to do with each other.The shaking steering wheel could be an out of balance or bad tire(torn belt),a bent wheel,or improperly tightened lug nuts(not torqued evenly).The check engine light will require a code scanner to see what the code is.(if you work on your own cars,you might want to buy at least an entry-level code reader/clearer,some are under 50 bucks).

Try rotating both front wheels to the back one at a time. If a tire has a bad belt; it may balanced but balancing does not eliminate a soft spot on the tire tread. By moving the tires to the back and road testing it after each side is done, you may be able to find the bad tire.

You have a lot of moving parts. A brake rotor could be out of balance, you can have a worn CV joint shaft, a hub bearing could be worn, driveshafts and U-joints can shake.

If you do find one wheel as a problem, have the tire dismounted and the wheel spun on the machine. You may have a bent rim and the tire may be good. Since the balance would help compensate for the vibration, it can mask the flattened spot on the rim. The tire will act like a shock absorber but ultimately the rim is not turning like it is round once weight is on it.

I would be interested in what you found.

Have the hubs inspected and the tires balanced. The wheel/tire assembly out of balance will cause the over 60 mph wobble/ steering wheel shake or drone. When did this occur or has it been going on for a while now?

I would start by having the tires carefully inspected and balanced if needed. A tire that has a broken internal steel cord can develop a lump or wave in the tread face which will cause the steering wheel to shake as the vehicle speed increases. Usually a tire that is developing such a problem is very close to failing completely [flat or blow-out] so have them checked as soon as possible. An out of balance tire usually just causes a general vibration or shake but can cause bigger problems depending on how out of balance they might be. Worn tie rod ends or other suspension components can cause a similar shake so have those items checked at the same time. Worn struts usually won't cause the shake you are describing but can cause the car to handle quite poorly and bounce excessively on bumpy roads. Wheel bearings often [but not always] make a grumbling/growling kind of noise as they start to go bad but usually won't cause a shake. A good inspection should quickly pinpoint the cause of the problem

did you retourque your wheels?

It sounds like you may have more than one problem here. First I would investigate Front End Alignment and ALL Steering/Suspension components for excessive wear and/or looseness. Second I would Inspect the Brake Rotors and Pads for uneven wear. Third I would check the Tires for uneven wear and balance. Many things can cause these symptoms: Worn out Ball Joints, defective Shock Absorbers/Struts. Worn out Tie Rod Ends, Idler Arm, even the Steering Gear Box can be part of the problem. Brake Rotors and Tires can be out of Balance with either one causing the problem over 60 MPH. I strongly suggest having your vehicle inspected by an ASE Certified Front End and Brake specialist immediately. It is very dangerous to drive a vehicle with these symptoms.

This is often the result of a tire that is out of balance. Check for bubbles on any of the tires and have the tires balanced. That should clear up the problem.

ball joint
control arm
shocks
brake rotor
and all your suspension parts have them check by your mechanic